In this paper, a numerical method is proposed for solving optimal control problem of Volterra integral equations using radial basis functions (RBFs) for approximating unknown function. Actually, the method is based on interpolation by radial basis functions including multiquadrics (MQs), to determine the control vector and the corresponding state vector in linear dynamic system while minimizing...

In the present paper, a numerical method is considered for solving one-dimensional heat equation subject to both Neumann and Dirichlet initial boundary conditions. This method is a combination of collocation method and radial basis functions (RBFs). The operational matrix of derivative for Laguerre-Gaussians (LG) radial basis functions is used to reduce the problem to a set of algebraic equatio...

The value algorithms of classical function approximation theory have a common drawback: the compute-intensive, poor adaptability, high model and data demanding and the limitation in practical applications. Neural network can calculate the complex relationship between input and output, therefore, neural network has a strong function approximation capability. This paper describes the application ...

We establish the functional equivalence of a generalized class of Gaussian radial basis function (RBFs) networks and the full Takagi-Sugeno model (1983) of fuzzy inference. This generalizes an existing result which applies to the standard Gaussian RBF network and a restricted form of the Takagi-Sugeno fuzzy system. The more general framework allows the removal of some of the restrictive conditi...

In this paper‎, ‎we decide to select the best center nodes‎ ‎of radial basis functions by applying the Multiple Criteria Decision‎ ‎Making (MCDM) techniques‎. ‎Two methods based on radial basis‎ ‎functions to approximate the solution of partial differential‎ ‎equation by using collocation method are applied‎. ‎The first is based‎ ‎on the Kansa's approach‎, ‎and the second is based on the Hermit...

In this paper, an innovative robust adaptive tracking control method for robotic systems with unknown dynamics using a nonlinearly parameterized Additive Recurrent Neural Network (ARNN) is proposed. The ARNN uses the Gaussian Radial Basis Functions (GRBF) as activation functions. Through this method the training laws of all GRBF parameters are determined. Additionally, the system is augmented w...

In this paper, we study the statistical properties of method of regularization with radial basis functions in the context of linear inverse problems. Radial basis function regularization is widely used in machine learning because of its demonstrated effectiveness in numerous applications and computational advantages. From a statistical viewpoint, one of the main advantages of radial basis funct...